Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

Continuous-wave quantum nondemolition measurements with vacuum and nonclassical meter input

QND measurements of the amplitude quadrature of continuous-wave light are performed with a monolithic dual-port degenerate optical parametric amplifier (OPA). Operated with a vacuum meter input, both output beams are squeezed and 33% correlated, demonstrating individually squeezed twin beams. The sum of the signal and meter transfer coefficients is 1.05, demonstrating operation as a quantum optical tap. The device exhibits quantum state preparation ability for both signal and meter output, reaching the conditional variances of dB and dB, respectively. An improved quantum measurement is realized by injecting 3.4 dB amplitude-squeezed light into the meter input port of the OPA. This achieves increased correlation and squeezing of the output beams, and both improved operation as a quantum optical tap and as a quantum state preparator. The all-solid-state system was operated for up to 5 hours with high stability. Received: 25 July 1996     

Generation of pulsed squeezed light in a mode-locked optical parametric oscillator

The generation of pulsed squeezed light using an optical parametric oscillator (OPO) is discussed. This mode-locked optical parametric oscillator consists of a nonlinear crystal in a cavity which is resonant for both signal and idler waves and which is synchronously pumped by the second-harmonic of an acousto-optically mode-locked cw Nd: YAG laser. The fundamental wavelength of the pump laser provides local oscillator pulses for balanced homodyne detection of squeezed vacuum pulses emitted by the oscillator when operated below oscillation threshold. Photocurrent noise reduction to 30% below the classical shot-noise limit is observed, corresponding to squeezing of the field to a level approximately a factor of two below the mean square vacuum noise.     

Two-mode squeezing in a coherently driven degenerate parametric down conversion

Squeezing properties of a two-mode radiation produced by a process of driven degenerate parametric down conversion, when the cavity is coupled to two independent squeezed vacuum reservoirs employing the linearization procedure, are analyzed. The two-mode cavity and output radiations exhibit considerable squeezing even when the oscillator is coupled to a vacuum reservoir. One of the effects of coupling the cavity to the squeezed vacuum reservoirs is to increase the degree of squeezing exponentially. For the output radiation the correlation of the quadrature operators evaluated at different times also contributes to the squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the fundamental mode.     

The atom-cavity system as a generator of quadrature squeezed states

This paper describes experiments with a coupled atom-cavity system generating quadrature squeezed states of light. A wide range of parameters was explored and a regime was found where a beam of laser light with significant power (0.17 mW) and good noise suppression (measured 18±3%, inferred 50±10%) was observed. An analysis of the exact phase of the noise suppression shows it to be a minimum uncertainty state with reduced noise in a combined amplitude/phase quadrature. The observations are in good qualitative agreement with a full quantum theory of squeezing in optical bistability.     

Quantum integrals of motion and gravity wave experiment: Measurements in pure quantum states

Quantum limitations arising in measurements of a classical force acting on a quantum harmonic oscillator are studied in connection with the problem of increasing the sensitivity of gravity wave experiments. The physical nature of possible limits of sensitivity is elucidated. It originates in a degree of an uncertainty of an observable used for detecting an external force. This uncertainty can be made as small as desired for all moments of time for the observables corresponding to quantum integrals of motion. Advantages of integrals of motion with continuous spectra (like the operator of the initial coordinate) over integrals with discrete spectra (like energy) are discussed. An example of an observable suitable for exact continuous measurements of an external force independently on the initial state of the system—the difference link operator—is given. The general rule for constructing such “optimal observables” can be derived from the quantum optimal filtration theory. It is shown using Ehrenfest's theorem that no quantum limitations exist in principle for the accuracy of measurements of an external classical force acting on an arbitrary quantum system: limitations can appear only due to nonadequate measuring procedures. The general problem of finding the initial quantum states possessing the best sensitivity to an external force is formulated. The parametrically excited oscillator is briefly discussed, and it is shown that measuring the suitable integral of motion one can achieve the great gain in sensitivity. The role of quantum interference effects is emphasized.     

Interaction of a two-level atom with squeezed light

We consider a degenerate parametric oscillator whose cavity contains a two-level atom. Applying the Heisenberg and quantum Langevin equations, we calculate in the bad-cavity limit the mean photon number, the quadrature variance, and the power spectrum for the cavity mode in general and for the signal light and fluorescent light in particular. We also obtain the normalized second-order correlation function for the fluorescent light. We find that the presence of the two-level atom leads to a decrease in the degree of squeezing of the signal light. It so turns out that the fluorescent light is in a squeezed state and the power spectrum consists of a single peak only.     

Repeated quantum non-demolition measurements

 We describe, in detail, theoretical and experimental aspects related to our recently reported repeated back-action evading measurements performed using two travelling-wave optical parametric amplifiers in series. The state of the observable being measured is almost perfectly preserved after two successive measurements. The final signal, and the intermediate measurement of the two successive setups are quantum correlated with conditional variances that lie in the quantum regime. Moreover, we show that the two independent measurements are quantum correlated up to 30%. Received: 11 April 1996/Revised version: 18 July 1996     

Laser cooling force in noisy quadrature of squeezed light

The laser cooling of atoms is a result of the combined effect of Doppler shift, light shift and polarization gradient. These are the phenomena which generally introduce frequency shift and uncertainty. However, they combine gainfully in realizing laser cooling and trapping of the atoms. In this paper we discuss the laser cooling of atoms in the presence of the squeezed light with the decay of atomic dipole moment into noisy quadrature. We show that the higher decay rate of the atomic dipole moment into the noisy quadrature, which leads to decrease in the signal to noise ratio, may contribute in realizing larger cooling force vis-à-vis with coherent laser light.     

Radiation noise of an active interferometer

 An investigation of the behaviour of amplitude and frequency noise of radiation of an active interferometer in the regime of amplified optical bistability is presented. The phenomenon of non-amplification of external signal noise at sharp amplification of the external signal is established. The impact of strong amplitude fluctuations is studied. Our results have shown that the active interferometer allows an effective separation of the valid signal from the amplitude noise. The spectral density of a fluctuation of the field frequency in the active interferometer is shown to fall sharply in comparison with the “quantum limit”. The linewidth of radiation is determined by the spectral density at zero frequency and is equal to the natural linewidth of the external signal. The influence of quantum noise of the amplifying and absorbing media of the active interferometer is discussed. Received: 26 January 1996     

铷原子D1线真空压缩光场的产生及态重构

碱金属原子是光量子存储的良好介质,与碱金属原子共振的非经典光场是量子信息处理的重要资源.本文采用周期极化磷酸氧钛晶体作为非线性介质,利用参量振荡过程产生了795 nm(铷原子D1线)的真空压缩光场.通过对平衡零拍探测系统的时域信号进行采集,得到压缩光场不同相位角下的噪声分布;利用极大似然估计法对压缩光场进行了态重构,得到了密度矩阵及相空间的Wigner函数.理论计算了真空压缩场的光子数分布和Wigner函数,并对理论计算结果和极大似然重构结果进行了分析和比较.     

纠缠微波信号的特性及表示方法

纠缠微波信号是电磁场微波频段量子特性的体现.在总结了现有纠缠微波信号产生及验证实验的基础上,针对目前没有统一的表达式来描述纠缠微波信号格式的问题,通过深入分析纠缠微波信号的特性,提出了两种纠缠微波信号的表示方法.一种是在量子框架下,利用双模压缩真空态表示,并分别在光子数表象下和Wigner分布下分析了其信号特征,刻画了正交分量之间的正反关联特性;另一种是在经典框架下,利用关联随机信号表示,刻画了测量后纠缠微波信号场幅度正交分量随时间变化的波形图.两种表示恰当合理地反映了纠缠微波信号连续变量纠缠的特性.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

A ponderomotive scheme for QND measurement of quadrature component

We propose a scheme for quantum nondemolition (QND) measurement of the quadrature component of a traveling wave, which uses the nonlinear ponderomotive interaction of electromagnetic waves reflected from a movable mirror. The influence of mechanical and optical losses and of imbalance in the interferometer arms is analyzed. Received: 27 March 1996 / Revised version: 25 September 1996     

Decoherence in atom–field interactions: A treatment using superoperator techniques

Decoherence is a subject of great importance in quantum mechanics, particularly in the fields of quantum optics, quantum information processing and quantum computing. Quantum computation relies heavily in the unitary character of each step carried out by a quantum computational device and this unitarity is affected by decoherence. An extensive study of master equations is therefore needed for a better understanding on how quantum information is processed when a system interacts with its environment. Master equations are usually studied by using Fokker–Planck and Langevin equations and not much attention has been given to the use of superoperator techniques. In this report we study in detail several approaches that lead to decoherence, for instance a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. For the study of the dissipative interaction we use a correspondence principle approach. We solve the master equations for different physical systems, namely, Kerr and parametric down conversion. In the case of light-matter interaction we show that although dissipation destroys the quantumness of the field, information of the initial field may be obtained via the reconstruction of quasiprobability distribution functions.     

低分析频率压缩光的实验制备

基于PPKTP晶体的阈值以下光学参量振荡(OPO)过程,制备了共振于铷原子D1线795 nm的压缩真空态光场,研究了分析频率处于千赫兹范围的主要噪声来源,特别是795 nm激光及其二次谐波397.5 nm激光在晶体内吸收引起的非线性损耗增加和系统热不稳定的问题(397.5 nm激光处于PPKTP晶体透光范围边缘,具有高于其他波长数倍的吸收系数).以795 nm和1064 nm为例,分析了非线性损耗及晶体内热效应对压缩度的影响.受限于以上因素,795 nm压缩光很难得到1064 nm波段同样的压缩度.探测系统中的噪声耦合则限制了压缩频带.实验上对分析频率为千赫兹的经典噪声进行了有效控制,通过使用真空注入的OPO、垂直偏振及反向传输的腔长锁定光、低噪声的平衡零拍探测器、高稳定度的实验系统及量子噪声锁定等方法,最终在2.6—100 kHz的分析频段得到了约2.8 dB的795 nm压缩真空.该压缩光可用作磁场测量系统的探测光以提高测量灵敏度.     

基于量子增强型光纤马赫-曾德尔干涉仪的低频信号测量

利用低频光通信波段真空压缩态光场可实现基于光纤的量子精密测量.本文利用简并光学参量振荡器实验制备出1550 nm低频真空压缩态光场.在分析频段10—500 kHz范围内压缩态光场的压缩度均达3 dB.用实验制备的1550 nm真空压缩态光场填补光纤马赫-曾德尔干涉仪的真空通道,实现了量子增强型光纤马赫-曾德尔干涉仪,完成了突破标准量子极限的相位调制频率为500 kHz的低频信号测量.与光纤马赫-曾德尔干涉仪相比,测量信噪比提高了2 dB.     

Heterodyne detection enhanced by quantum correlation

Heterodyne detectors as phase-insensitive(PI) devices have found important applications in precision measurements such as space-based gravitational-wave(GW) observation. However, the output signal of a PI heterodyne detector is supposed to suffer from signal-to-noise ratio(SNR) degradation due to image band vacuum and imperfect quantum efficiency. Here, we show that the SNR degradation can be overcome when the image band vacuum is quantum correlated with the input signal.We calculate the noise figure of the detector and prove the feasibility of heterodyne detection with enhanced noise performance through quantum correlation. This work should be of great interest to ongoing space-borne GW signal searching experiments.     

高灵敏度的量子迈克耳孙干涉仪

迈克耳孙干涉仪不仅可以用来研究物理学的基本问题,而且能够用于精密测量,比如引力波信号的测量.因此,构建高灵敏度的迈克耳孙干涉仪是实现微弱信号测量的关键.目前,人们利用压缩态可以降低迈克耳孙干涉仪的噪声;通过光学四波混频过程能够放大马赫·曾德尔干涉仪中的相位信号,从而提高干涉仪的信噪比和灵敏度.本文研究了一种用于高灵敏度相位测量的量子迈克耳孙干涉仪.在迈克耳孙干涉仪中,利用非简并光学参量放大器取代干涉仪中的线性光学分束器;并且将压缩态注入干涉仪的真空通道,可以得到高信噪比和高灵敏度的干涉仪.由于存在不可避免的光学损耗,分析了迈克耳孙干涉仪内部和外部的损耗对相位测量灵敏度的影响.通过理论计算研究了干涉仪的相位测量灵敏度随系统参数的变化关系,得到了高灵敏度的相位测量量子迈克耳孙干涉仪的实现条件,为用于精密测量的干涉仪的设计提供了直接参考.